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Influence of charge changing processes on the forward to backward electron emission yield ratio for light ions impinging on thin metallic foils
Nuclear Instruments and Methods in Physics Research B 212 (2003) 391–396 www.elsevier.com/locate/nimb
Influence of charge changing processes on the forward to backward electron emission yield ratio for light ions impinging on thin metallic foils N. Pauly a
a,*
, A. Dubus a, M. R€ osler
b
Universit e Libre de Bruxelles, Service de M etrologie Nucl eaire (CP 165/84), 50 av. F.D. Roosevelt, B-1050 Brussels, Belgium b Hahn-Meitner-Institut Berlin, Glienicker Str. 100, D-14109 Berlin, Germany
Abstract Stopping power dE=dx and electron emission yield c are known to be strongly influenced by electron capture and loss processes. In this work we consider proton impact on thin Al foils for impact velocities below two atomic units. We investigate the effect of the charge changing processes on the forward/backward electron emission yields, cF and cB as well as on the specific yields, KF and KB ðK ¼ c=ðdE=dxÞÞ. The dependence of the emission yields and of the specific yields as a function of the target thickness is discussed in terms of the charge changing processes. Ó 2003 Elsevier B.V. All rights reserved. PACS: 79.20.Rf Keywords: Particle induced electron emission; Charge exchange processes
1. Introduction Kinetic ion induced electron emission (KIIEE) has been the object of many theoretical [1] and experimental [2] studies. In the particular case of thin targets, the ions can cross the foil and electrons are emitted from both surfaces of the target. Electron emission from the entrance surface is called backward emission whereas electron emission from the exit surface is called forward emission. Forward and backward emissions have been the object of many measurements in the particular *
Corresponding author. Tel.: +32-2-6502097; fax: +32-26504534. E-mail address: [email protected] (N. Pauly).
case of thin carbon foils and with various incident projectiles such as protons [3,4], heavy ions [5] and clusters [4,6]. For other targets, only a few measurements exist. Rothard et al. [3] for instance have measured forward and backward electron emission characteristics for various projectiles incident on thin C, Al, Ti, Ni and Cu targets. An interesting quantity first determined by Meckbach et al. [7] and Meckbach [8] is the ratio Rc ¼ cF =cB between the forward (cF ) and the backward (cB ) electron emission yields. Rothard et al. [9] have called Rc the ‘‘Meckbach factor’’ and we will use this notation in the following. The measurement of the forward and backward emission characteristics and in particular of Rc provides lots of information about the electron excitation by the incident projectile as well as
0168-583X/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0168-583X(03)01511-8
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N. Pauly et al. / Nucl. Instr. and Meth. in Phys. Res. B 212 (2003) 391–396
about electron transport effects. Forward and backward emissions are also strongly influenced by the electron capture and loss processes (see [10] for instance), in particular in the intermediate projectile velocity range (v ’ 1 a.u.) where charge changing processes are known to play an important role [11]. Another interesting quantity in KIIEE is the ratio between the electron emission yield c and the stopping power ðdE=dxÞ. This quantity K ¼ c=ðdE=dxÞ is called the specific yield [2]. In the particular case of electron emission from thin foils, once again two specific yields can be determined, i.e. the forward and backward specific yields KF ¼ cF =ðdE=dxÞ and KB ¼ cB =ðdE=dxÞ. The backward specific yield KB has been shown by Hasselkamp for instance [12], in the case of protons incident on various metallic targets, to be more or less independent of the incident projectile energy. Baragiola [13] has even proposed an av for KB with an uncertainty erage value of 0.1 eV/A of 30% for protons incident on metals. The more or less constant ratio of the electron emission yield and the stopping power has been at the basis of two important ‘‘macroscopic’’ models proposed by Sternglass [14] and Schou [15,16]. However, even if kinetic electron emission and electronic stopping power are two aspects of the same phenomenon, i.e. energy loss in electron excitation by the incident projectile, there is no a priori reason why the specific yield K should be constant. This is particularly true when considering the forward specific yield KF . Beuve et al. [17] and Dubus et al. [18] have studied the forward and backward specific yields for protons (MeV range) incident on thin carbon foil and have shown that KF was increasing or decreasing with the incident projectile energy, depending on the foil thickness. This effect was explained by electron transport. Electron capture and loss processes also influence the specific yields KF and KB , in particular in the intermediate velocity range. It is precisely the aim of this work to incorporate the charge changing processes in a Monte Carlo (MTC) simulation to obtain the backward and forward electron emission yields for protons with energy varying between 25 and 100 keV (1 a:u: 6 v 6 2 a.u.) incident on thin polycrystalline
aluminium targets. Most experimental results exist for carbon foils. We have nevertheless preferred to present theoretical results for aluminium targets because the present state of the theoretical description of charged particle interactions in amorphous carbon is more questionable even if good results have been obtained by Beuve et al. [17] and Dubus et al. [18] for instance. We will then limit comparisons with experiments to qualitative comparisons. We describe in the following the theoretical model that we have used for the calculation of the electron emission characteristics for protons incident on thin aluminium targets in the 1–2 a.u. velocity range. Then, we present the calculated forward and backward yields cF and cB as well as the forward and backward specific yields KF and KB . The target thickness dependence of these coefficients is also presented as well as the influence of charge changing processes on all these quantities.
2. Theoretical description of the interaction mechanisms The theoretical model used to calculate electron emission for protons incident on aluminium targets has already been described elsewhere [19]. We briefly outline here the main aspects of this model. An analogue MTC simulation is used to describe electron excitation by the incident projectile and excited electron interactions and transport in the target [20]. We will consider here targets thin enough so that the ions cross the foils with negligible energy loss and angular deflections. For 25 keV Al foil (typical value), protons incident on a 300 A the energy loss is indeed 3 keV. This fraction of the incident projectile energy is not negligible but the error due to the neglect of this energy loss is not too important. For the incident protons, we have then two kinds of processes to consider, i.e. electron excitations without charge changing processes and charge changing processes, the latter giving of course rise to additional electron excitation. Three different mechanisms are considered to be responsible for the charge changing processes [11]. The first mechanism is the Auger process, in which
N. Pauly et al. / Nucl. Instr. and Meth. in Phys. Res. B 212 (2003) 391–396
an electron is captured (lost) by the ion to (from) a bound state assisted by a third body (plasmon or valence band electron). The second one is the resonant coherent process: the electronic exchange is induced by the crystal potential as seen from the moving projectile. The third process is the shell process: an inner-shell electron from the target is captured in a bound state by the moving ion. Various potentials can be used to describe the resonant coherent processes. The choice of the potential has been shown to influence the resonant coherent cross-section as has been discussed by Pauly et al. [21]. Pauly et al. [19] have however shown that this choice did not really influence the calculated electron emission characteristics for incident protons on Al targets in the velocity range considered here. In this work, we have chosen the Hartree potential [21] or an effective potential deduced from phase shifts calculated in LEED [11]. We have also considered that the proton could exits in the target with three different charge states: Hþ , H0 and H . The existence of H inside the target is still the object of discussions. We will take its possibility of existence into account but as we will see below, the influence of H on the results is negligible. For the electron excitation by the incident projectile, we have considered electron excitation from the valence bands of aluminium within the dielectric formalism of Lindhard [22]. The structure of the projectile was taken into account for H0 and H (see [23] for instance). We have neglected inner-shell ionizations due to the low projectile velocities considered in this work. For the interactions of electrons, we have once again considered electron interaction with the valence bands of aluminium and neglected innershell ionizations. We have also considered elastic collisions calculated from a muffin-tin potential tabulated by Smrcka [24]. The stopping power that we have used to calculate the specific yield has been taken from [25].
3. MTC results We present in Fig. 1 the forward (the thickness of the target has been supposed large enough so that charge state equilibrium is reached for the
393
Fig. 1. Backward and forward electron emission yields as a function of the velocity: in a frozen charge state: backward (n) and forward (h) and with charge changing processes: backward (}) and forward (). We present also the backward yield with charge changing processes with a LEED potential (O).
forward yield and small enough so that energy losses and angular deflections for the incident projectile can be neglected) and backward electron emission yields cF and cB with and without charge changing processes. For both the forward and backward yields, we have performed the calculations including and neglecting H charge state. We have not obtained any significant influence due to the presence of H in the target. Two different choices have been made for the potential with which we have calculated the resonant coherent cross-section, i.e. the Hartree potential and a LEED potential (see above). As has already been obtained by Pauly et al. [19], the influence of charge changing processes on the backward yield is small. The influence of this choice is obviously negligible. The influence of the charge state on the forward yield is on the contrary important especially for the smallest velocities considered here. As has already been discussed in [19], for backward emission, the decrease of the yield due to the fact that Hþ becomes H0 for a part of its trajectory in the depth zone from which electrons can escape is counterbalanced by the contribution to the backward yield of all additional electrons excited during the charge changing processes. For the forward yield, charge changing processes have a strong influence in particular due to the charge distribution of exiting projectiles. This is particularly
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N. Pauly et al. / Nucl. Instr. and Meth. in Phys. Res. B 212 (2003) 391–396
Fig. 2. Meckbach factor as a function of the velocity: without charge changing (h) and with charge changing (). We present also the Meckbach experimental result for Hþ incident on carbon foils.
true for the smallest velocities considered here while for the largest velocities, the Hþ fraction at equilibrium becomes close to 1 [26] and the electron captures become improbable. The forward yield is larger than the backward yield for almost all the velocities due to the fact that the electrons are excited mainly in the forward direction. We show in Fig. 2 the Meckbach factor Rc and in Fig. 3 the specific yields KF and KB . For the Meckbach factor, the influence of the charge changing processes is obviously very im-
Fig. 3. Backward (h) and forward (n) specific yield as a function of the velocity with charge changing processes. We give also the experimental result of Hasselkamp for the backward specific yield (solid line).
portant, as a consequence of the influence of these processes on the forward yield. When the charge changing processes are considered, our simulation result is qualitatively in agreement with the experimental results of Meckbach et al. [7] and Meckback for Hþ incident on carbon targets. Our result for the backward specific yield is in qualitative agreement with the experimental result of Hasselkamp [12]. For the forward specific yield, the only experimental results for aluminium are those of Rothard et al. [3]. However, the backward ) are in disspecific yields they obtain (0.4 eV/A agreement with all other experimental results so that no comparison with these results was possible. We have investigated the influence of the target thickness on the forward and backward electron emission yields (see Fig. 4). We present on Fig. 4(a) our results for cB for thicknesses of 20, 10, 5, 2 (these values being totally unrealistic in a and 1 A practical way). The results for cF have the same behavior. We observe a decrease of the yields when the thickness of the target is decreased only for . For 20 A , we have more or thicknesses below 10 A less the same result as for a target with a thickness . These results are qualitatively in agreeof 300 A ment with experimental results obtained for carbon targets for higher energies (1.2 MeV) [4,27]. Only for very small thicknesses a decrease of the yields is observable. We present also (Fig. 4(b)) the evolution of the Meckbach factor Rc for the same thicknesses. Rc is clearly increasing with the decrease of the thickness. The forward yield decreases more slowly with the thickness than the backward yield. Moreover, we notice that the Meckbach factor is more or less constant as a function of the incident projectile velocity for large thicknesses and decreases with the velocity of the ion for small thicknesses. Indeed, the electrons are excited preferentially in the forward direction for small velocities and more perpendicularly to the ion trajectory for higher energies (but always in the forward direction) [28]. For the backward yield, electron cascade is necessary for electrons to be emitted. Such cascade is only possible for thick enough targets. For the forward yield, electron cascade also plays a role but a contribution of directly emitted electrons also exists. Hence, for very small target thicknesses, the Meckbach factor
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thickness of the targets on our results. This influence is in agreement with previously published results.
References
Fig. 4. (a) Backward electron yield as a function of the velocity for different thicknesses of the aluminium target. We consider (), 10 A (n), 5 A (h), 2 A (}) and 1 A thicknesses of 20 A (O). We indicate also the result for a thick target. (b) Ratio Rc as a function of the velocity for different thicknesses. We con (), 10 A (n), 5 A (h), 2 A (}) and 1 A (O). sider 20 A
is larger than for larger thicknesses. This is particularly true for small velocities.
4. Conclusions We have shown in this paper the effects of charge changing processes on the backward and forward electron emission from aluminium targets induced by incident protons with energy between 25 and 100 keV. For the same cases, we have also presented the Meckbach factor and the specific yields considering these charge changing processes. Moreover, we have show the influence of the
[1] M. R€ osler, W. Brauer, J. Devooght, J.-C. Dehaes, A. Dubus, M. Cailler, J.-P. Ganachaud, in: G. H€ ohler, E.A. Niekisch (Eds.), Particle Induced Electron Emission I, Springer Tracts in Modern Physics, Vol. 122, SpringerVerlag, Berlin, 1991. [2] D. Hasselkamp, H. Rothard, K.O. Groeneveld, J. Kemmler, P. Varga, H. Winter, in: G. H€ ohler, E.A. Niekisch (Eds.), Particle Induced Electron Emission II, Springer Tracts in Modern Physics, Vol. 123, Springer-Verlag, Berlin, 1992. [3] H. Rothard, K. Kroneberger, A. Clouvas, E. Veje, P. Lorenzen, N. Keller, J. Kemmler, W. Meckbach, K.-O. Groeneveld, Phys. Rev. A 41 (1990) 2521. [4] H. Rothard, K. Kroneberger, E. Veje, A. Clouvas, J. Kemmler, P. Koschar, N. Keller, S. Lencinas, P. Lorenzen, O. Heil, D. Hofmann, K.-O. Groeneveld, Phys. Rev. B 41 (1990) 3959. [5] H. Rothard, C. Caraby, A. Cassimi, B. Gervais, J.-P. Grandin, P. Jardin, M. Jung, Phys. Rev. A 51 (1995) 3066. [6] A. Billebaud, M. Fallavier, R. Kirsch, J.-C. Poizat, J. Remilleux, Z. Vidovic, Phys. Rev. A 55 (1997) 1124. [7] W. Meckbach, G. Braunstein, N. Arista, J. Phys. B 8 (1975) L344. [8] W. Meckbach, in: I.A. Sellin, D.J. Pegg (Eds.), Beam-Foil Spectroscopy, Plenum Press, New York, 1976, p. 577. [9] H. Rothard, J. Schou, K.-O. Groeneveld, Phys. Rev. A 45 (1992) 1701. [10] C. Smidts, A. Dubus, J.-C. Dehaes, A. Hafni, J.P. Ganachaud, Nucl. Instr. and Meth. B 67 (1992) 646. [11] P.M. Echenique, F. Flores, R.H. Ritchie, in: H. Ehrenreich, D. Turnbull (Eds.), Solid State Physics, Vol. 43, Academic Press, New York, 1990, p. 229. [12] D. Hasselkamp, in [2], p. 1. [13] R.A. Baragiola, E.V. Alonso, J. Ferr on, A. Oliva-Florio, Surf. Sci. 90 (1979) 240. [14] E.J. Sternglass, Phys. Rev. 108 (1957) 1. [15] J. Schou, Phys. Rev. B 22 (1980) 2141. [16] J. Schou, Scanning Microsc. 2 (1988) 607. [17] M. Beuve, M. Caron, B. Gervais, H. Rothard, A. Clouvas, C. Potiriadis, Eur. Phys. J. D 15 (2001) 293. [18] A. Dubus, N. Pauly, M. R€ osler, H. Rothard, M. Beuve, M. Caron, B. Gervais, A. Clouvas, C. Potiriadis, Nucl. Instr. and Meth. B 193 (2002) 621. [19] N. Pauly, A. Dubus, M. R€ osler, Nucl. Instr. and Meth. B 203 (2003) 36. [20] A. Dubus, M. R€ osler, O. Benka, Math. Comput. Simul. 55 (2001) 37. [21] N. Pauly, A. Dubus, M. R€ osler, J. Electron, Spectrosc. Relat. Phenom. 129 (2003) 229.
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[22] J. Lindhard, Mat. Fys. Medd. Dan. Vid. Selsk. 28 (1954) 1. [23] A. Dubus, M. R€ osler, Nucl. Instr. and Meth. B 125 (1997) 18. [24] L. Smrcka, Czech. J. Phys. B 20 (1970) 291. [25] Stopping Powers and Ranges fot Protons and Alpha Particles, ICRU Report 49, 1993. [26] F. Flores, in: A. Gras-Martı, H.M. Urbassek, N.R. Arista, F. Flores (Eds.), Interaction of Charged Particles with
Solids and Surfaces, Plenum Press, New York, 1991, p. 3. [27] K. Kroneberger, A. Clouvas, G. Schl€ usser, P. Koschar, J. Kemmler, H. Rothard, C. Biedermann, O. Heil, M. Burkhard, K.O. Groeneveld, Nucl. Instr. and Meth. B 29 (1988) 621. [28] D.K. Brice, P. Sigmund, Mat. Fys. Medd. Dan. Vid. Selsk. 40 (1980) 1.
Influence of charge changing processes on the forward to backward electron emission yield ratio for light ions impinging on thin metallic foils N. Pauly a
a,*
, A. Dubus a, M. R€ osler
b
Universit e Libre de Bruxelles, Service de M etrologie Nucl eaire (CP 165/84), 50 av. F.D. Roosevelt, B-1050 Brussels, Belgium b Hahn-Meitner-Institut Berlin, Glienicker Str. 100, D-14109 Berlin, Germany
Abstract Stopping power dE=dx and electron emission yield c are known to be strongly influenced by electron capture and loss processes. In this work we consider proton impact on thin Al foils for impact velocities below two atomic units. We investigate the effect of the charge changing processes on the forward/backward electron emission yields, cF and cB as well as on the specific yields, KF and KB ðK ¼ c=ðdE=dxÞÞ. The dependence of the emission yields and of the specific yields as a function of the target thickness is discussed in terms of the charge changing processes. Ó 2003 Elsevier B.V. All rights reserved. PACS: 79.20.Rf Keywords: Particle induced electron emission; Charge exchange processes
1. Introduction Kinetic ion induced electron emission (KIIEE) has been the object of many theoretical [1] and experimental [2] studies. In the particular case of thin targets, the ions can cross the foil and electrons are emitted from both surfaces of the target. Electron emission from the entrance surface is called backward emission whereas electron emission from the exit surface is called forward emission. Forward and backward emissions have been the object of many measurements in the particular *
Corresponding author. Tel.: +32-2-6502097; fax: +32-26504534. E-mail address: [email protected] (N. Pauly).
case of thin carbon foils and with various incident projectiles such as protons [3,4], heavy ions [5] and clusters [4,6]. For other targets, only a few measurements exist. Rothard et al. [3] for instance have measured forward and backward electron emission characteristics for various projectiles incident on thin C, Al, Ti, Ni and Cu targets. An interesting quantity first determined by Meckbach et al. [7] and Meckbach [8] is the ratio Rc ¼ cF =cB between the forward (cF ) and the backward (cB ) electron emission yields. Rothard et al. [9] have called Rc the ‘‘Meckbach factor’’ and we will use this notation in the following. The measurement of the forward and backward emission characteristics and in particular of Rc provides lots of information about the electron excitation by the incident projectile as well as
0168-583X/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0168-583X(03)01511-8
392
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about electron transport effects. Forward and backward emissions are also strongly influenced by the electron capture and loss processes (see [10] for instance), in particular in the intermediate projectile velocity range (v ’ 1 a.u.) where charge changing processes are known to play an important role [11]. Another interesting quantity in KIIEE is the ratio between the electron emission yield c and the stopping power ðdE=dxÞ. This quantity K ¼ c=ðdE=dxÞ is called the specific yield [2]. In the particular case of electron emission from thin foils, once again two specific yields can be determined, i.e. the forward and backward specific yields KF ¼ cF =ðdE=dxÞ and KB ¼ cB =ðdE=dxÞ. The backward specific yield KB has been shown by Hasselkamp for instance [12], in the case of protons incident on various metallic targets, to be more or less independent of the incident projectile energy. Baragiola [13] has even proposed an av for KB with an uncertainty erage value of 0.1 eV/A of 30% for protons incident on metals. The more or less constant ratio of the electron emission yield and the stopping power has been at the basis of two important ‘‘macroscopic’’ models proposed by Sternglass [14] and Schou [15,16]. However, even if kinetic electron emission and electronic stopping power are two aspects of the same phenomenon, i.e. energy loss in electron excitation by the incident projectile, there is no a priori reason why the specific yield K should be constant. This is particularly true when considering the forward specific yield KF . Beuve et al. [17] and Dubus et al. [18] have studied the forward and backward specific yields for protons (MeV range) incident on thin carbon foil and have shown that KF was increasing or decreasing with the incident projectile energy, depending on the foil thickness. This effect was explained by electron transport. Electron capture and loss processes also influence the specific yields KF and KB , in particular in the intermediate velocity range. It is precisely the aim of this work to incorporate the charge changing processes in a Monte Carlo (MTC) simulation to obtain the backward and forward electron emission yields for protons with energy varying between 25 and 100 keV (1 a:u: 6 v 6 2 a.u.) incident on thin polycrystalline
aluminium targets. Most experimental results exist for carbon foils. We have nevertheless preferred to present theoretical results for aluminium targets because the present state of the theoretical description of charged particle interactions in amorphous carbon is more questionable even if good results have been obtained by Beuve et al. [17] and Dubus et al. [18] for instance. We will then limit comparisons with experiments to qualitative comparisons. We describe in the following the theoretical model that we have used for the calculation of the electron emission characteristics for protons incident on thin aluminium targets in the 1–2 a.u. velocity range. Then, we present the calculated forward and backward yields cF and cB as well as the forward and backward specific yields KF and KB . The target thickness dependence of these coefficients is also presented as well as the influence of charge changing processes on all these quantities.
2. Theoretical description of the interaction mechanisms The theoretical model used to calculate electron emission for protons incident on aluminium targets has already been described elsewhere [19]. We briefly outline here the main aspects of this model. An analogue MTC simulation is used to describe electron excitation by the incident projectile and excited electron interactions and transport in the target [20]. We will consider here targets thin enough so that the ions cross the foils with negligible energy loss and angular deflections. For 25 keV Al foil (typical value), protons incident on a 300 A the energy loss is indeed 3 keV. This fraction of the incident projectile energy is not negligible but the error due to the neglect of this energy loss is not too important. For the incident protons, we have then two kinds of processes to consider, i.e. electron excitations without charge changing processes and charge changing processes, the latter giving of course rise to additional electron excitation. Three different mechanisms are considered to be responsible for the charge changing processes [11]. The first mechanism is the Auger process, in which
N. Pauly et al. / Nucl. Instr. and Meth. in Phys. Res. B 212 (2003) 391–396
an electron is captured (lost) by the ion to (from) a bound state assisted by a third body (plasmon or valence band electron). The second one is the resonant coherent process: the electronic exchange is induced by the crystal potential as seen from the moving projectile. The third process is the shell process: an inner-shell electron from the target is captured in a bound state by the moving ion. Various potentials can be used to describe the resonant coherent processes. The choice of the potential has been shown to influence the resonant coherent cross-section as has been discussed by Pauly et al. [21]. Pauly et al. [19] have however shown that this choice did not really influence the calculated electron emission characteristics for incident protons on Al targets in the velocity range considered here. In this work, we have chosen the Hartree potential [21] or an effective potential deduced from phase shifts calculated in LEED [11]. We have also considered that the proton could exits in the target with three different charge states: Hþ , H0 and H . The existence of H inside the target is still the object of discussions. We will take its possibility of existence into account but as we will see below, the influence of H on the results is negligible. For the electron excitation by the incident projectile, we have considered electron excitation from the valence bands of aluminium within the dielectric formalism of Lindhard [22]. The structure of the projectile was taken into account for H0 and H (see [23] for instance). We have neglected inner-shell ionizations due to the low projectile velocities considered in this work. For the interactions of electrons, we have once again considered electron interaction with the valence bands of aluminium and neglected innershell ionizations. We have also considered elastic collisions calculated from a muffin-tin potential tabulated by Smrcka [24]. The stopping power that we have used to calculate the specific yield has been taken from [25].
3. MTC results We present in Fig. 1 the forward (the thickness of the target has been supposed large enough so that charge state equilibrium is reached for the
393
Fig. 1. Backward and forward electron emission yields as a function of the velocity: in a frozen charge state: backward (n) and forward (h) and with charge changing processes: backward (}) and forward (). We present also the backward yield with charge changing processes with a LEED potential (O).
forward yield and small enough so that energy losses and angular deflections for the incident projectile can be neglected) and backward electron emission yields cF and cB with and without charge changing processes. For both the forward and backward yields, we have performed the calculations including and neglecting H charge state. We have not obtained any significant influence due to the presence of H in the target. Two different choices have been made for the potential with which we have calculated the resonant coherent cross-section, i.e. the Hartree potential and a LEED potential (see above). As has already been obtained by Pauly et al. [19], the influence of charge changing processes on the backward yield is small. The influence of this choice is obviously negligible. The influence of the charge state on the forward yield is on the contrary important especially for the smallest velocities considered here. As has already been discussed in [19], for backward emission, the decrease of the yield due to the fact that Hþ becomes H0 for a part of its trajectory in the depth zone from which electrons can escape is counterbalanced by the contribution to the backward yield of all additional electrons excited during the charge changing processes. For the forward yield, charge changing processes have a strong influence in particular due to the charge distribution of exiting projectiles. This is particularly
394
N. Pauly et al. / Nucl. Instr. and Meth. in Phys. Res. B 212 (2003) 391–396
Fig. 2. Meckbach factor as a function of the velocity: without charge changing (h) and with charge changing (). We present also the Meckbach experimental result for Hþ incident on carbon foils.
true for the smallest velocities considered here while for the largest velocities, the Hþ fraction at equilibrium becomes close to 1 [26] and the electron captures become improbable. The forward yield is larger than the backward yield for almost all the velocities due to the fact that the electrons are excited mainly in the forward direction. We show in Fig. 2 the Meckbach factor Rc and in Fig. 3 the specific yields KF and KB . For the Meckbach factor, the influence of the charge changing processes is obviously very im-
Fig. 3. Backward (h) and forward (n) specific yield as a function of the velocity with charge changing processes. We give also the experimental result of Hasselkamp for the backward specific yield (solid line).
portant, as a consequence of the influence of these processes on the forward yield. When the charge changing processes are considered, our simulation result is qualitatively in agreement with the experimental results of Meckbach et al. [7] and Meckback for Hþ incident on carbon targets. Our result for the backward specific yield is in qualitative agreement with the experimental result of Hasselkamp [12]. For the forward specific yield, the only experimental results for aluminium are those of Rothard et al. [3]. However, the backward ) are in disspecific yields they obtain (0.4 eV/A agreement with all other experimental results so that no comparison with these results was possible. We have investigated the influence of the target thickness on the forward and backward electron emission yields (see Fig. 4). We present on Fig. 4(a) our results for cB for thicknesses of 20, 10, 5, 2 (these values being totally unrealistic in a and 1 A practical way). The results for cF have the same behavior. We observe a decrease of the yields when the thickness of the target is decreased only for . For 20 A , we have more or thicknesses below 10 A less the same result as for a target with a thickness . These results are qualitatively in agreeof 300 A ment with experimental results obtained for carbon targets for higher energies (1.2 MeV) [4,27]. Only for very small thicknesses a decrease of the yields is observable. We present also (Fig. 4(b)) the evolution of the Meckbach factor Rc for the same thicknesses. Rc is clearly increasing with the decrease of the thickness. The forward yield decreases more slowly with the thickness than the backward yield. Moreover, we notice that the Meckbach factor is more or less constant as a function of the incident projectile velocity for large thicknesses and decreases with the velocity of the ion for small thicknesses. Indeed, the electrons are excited preferentially in the forward direction for small velocities and more perpendicularly to the ion trajectory for higher energies (but always in the forward direction) [28]. For the backward yield, electron cascade is necessary for electrons to be emitted. Such cascade is only possible for thick enough targets. For the forward yield, electron cascade also plays a role but a contribution of directly emitted electrons also exists. Hence, for very small target thicknesses, the Meckbach factor
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thickness of the targets on our results. This influence is in agreement with previously published results.
References
Fig. 4. (a) Backward electron yield as a function of the velocity for different thicknesses of the aluminium target. We consider (), 10 A (n), 5 A (h), 2 A (}) and 1 A thicknesses of 20 A (O). We indicate also the result for a thick target. (b) Ratio Rc as a function of the velocity for different thicknesses. We con (), 10 A (n), 5 A (h), 2 A (}) and 1 A (O). sider 20 A
is larger than for larger thicknesses. This is particularly true for small velocities.
4. Conclusions We have shown in this paper the effects of charge changing processes on the backward and forward electron emission from aluminium targets induced by incident protons with energy between 25 and 100 keV. For the same cases, we have also presented the Meckbach factor and the specific yields considering these charge changing processes. Moreover, we have show the influence of the
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